Not a secret: there is a shootable button at the entrance. It opens a pit right underneath. Goodie inside.

When you see the gravity belt, look to the ceiling right. There is a red button. Shooting it opens an room.

After finishing with The Mummy, stand in the remains of his coffin (and him!) and look left and right. There are two sarcophagus visible. Behind one, there is a rather badly concealed teleporter - one of many - to the maze upstairs.
Behind the other, you will find a Quad. Hm. Perhaps you should have picked this one up _before_ the argument with the mummy...
Thanks to Mauritorami for this hint!

No wonder that Pharaoh never found the Americas. Building a boat on first floor inside a stone block... Get on the port railing astern, you can see some steps. Get topside, and pick up a goodie.

Upstairs, after the mazes, there is a cobra statue. Facing it is a obelisk with a red light. Shoot the light. The cobra moves, jump into the hole in the floor before it shuts again.

There are another cobra/obelisk in the other end of the corridor. Same procedure...

At the exit, shoot the left wall. Teleporter behind it, leading to the last secret.